Gravitational dipole moment from an exact solution with torsion

TL;DR

This paper presents an exact solution to gravitational field equations with torsion that models a gravitational dipole without requiring negative mass, potentially impacting dark matter theories.

Contribution

It introduces a novel exact solution with torsion using a non-symmetric metric tensor that exhibits a gravitational dipole without negative mass.

Findings

The solution features a singularity at the origin.

No event horizon is present in the solution.

Gravitational dipoles could help explain dark matter.

Abstract

Dipole fields are common in electromagnetism and may be viewed as the result of a positive and negative charge (or pole) which are close together. A dipole field in gravity is not expected to exist because negative mass has never been observed. However, an exact solution to the gravitational field equations with torsion is presented that does correspond to a dipole gravitational field, even though there is no negative mass. The theory is based on a non-symmetric metric tensor, and it is found there is a singularity in the metric tensor at the origin but no event horizon. Gravitational dipoles have been used to solve the dark matter problem.